Yes, this is the only way.

Recently in 2019, I have done this in Scotland. You might be aware that if you are in Tier 2 and want to continue in Tier 2, you must find another sponsor or leave the country. If you leave the country, you cannot apply another visa for a year due to the cool-off period. For your case, it is unlikely to extend your contract if there is no fund left but talk about on this with your PI if it is possible. I know another Marie-Currie who had an extension on his contract so can keep the salary payments. 

In my case, there was not any fund left so I decided to finish and applied for student visa. So this is kind of new application and extension visa which is weird. Be aware, this requires new ATAS so start to prepare at least 3 months before your visa expired. 

For further career options, if you continue your career in the UK, the cool-off does not apply to this case (Tier 2>Tier 4>Tier 2). My current institution discovered that with Home Office in a month period so keep in mind. 
Best